An application of unfolding and cumulative item response theory models for noncognitive scaling : examining the assumptions and applicability of the generalized graded unfolding model

This study examined the applicability of a relatively new unidimensional, unfolding item response theory (IRT) model called the generalized graded unfolding mode. A total of four scaling methods were applied. Two commonly used cumulative IRT models for polytomous data, the Partial Credit Model and the Generalized Partial Credit model were considered. The third scaling approach was the use of a confirmatory factor analysis. The fourth model, an unfolding IRT model, the Generalized Graded Unfolding Model was considered. These models were applied to attitudinal data from 65,031 licensed teachers in North Carolina who responded to a survey about their working conditions. Two subscales (Empowerment and Leadership) were used and analyzed separately. Items are Likert-type with five response options ranging from Strongly Agree to Strongly Disagree. Analyses focused on examination of the correspondence between the assumptions that underlie the data and the IRT models, revealing evidence about the structure of the data, the location of people and items, and the response process governing observed data. The analyses included graphical representations of person and item estimates as well as analytical examination of item characteristic curves (ICCs) for the various models. Various indices of relative and absolute model fit statistics are presented for the IRT models. Although the two scales were originally built using factor analytic methods, results suggested that a single factor model did not fit the Empowerment well, though fit of the Leadership data was moderate. Tests of IRT model assumptions indicated that cumulative assumptions were meet more often than those that underlie unfolding IRT models. Comparison of item and person parameter estimates show that, across both scales, cumulative and unfolding IRT models functioned very similarly. However, some item on both scales did exhibit unfolding properties. Finally, a summary of potential extensions of the GGUM model and other contributions of this research including the possibility of using unfolding models for scale development and attitude measurement in areas beyond that of working conditions of teachers or administrators are offered.